In AngularJS, expressions can directly call functions defined in the Controller scope. The Controller scope holds the application data and functions, and expressions can access and invoke these functions directly. This feature enhances the flexibility of AngularJS applications by allowing seamless integration of logic defined in the Controller with the HTML templates.

The primary purpose of data binding in AngularJS controllers is to establish a connection between the model and the view. Data binding allows automatic synchronization of data between these two layers, ensuring that changes in the model are reflected in the view and vice versa. This simplifies the process of keeping the user interface up-to-date with the underlying data and enhances the responsiveness of AngularJS applications. Understanding data binding is fundamental to building dynamic and interactive user interfaces.

In AngularJS, handling global events in controllers can be achieved using $rootScope. While $rootScope provides a way to broadcast events globally, developers should be cautious about its impact on application performance. Broadcasting global events can lead to increased coupling between components and potential performance bottlenecks. Understanding the trade-offs is essential for maintaining a well-performing AngularJS application.

In AngularJS, you apply a controller to a specific part of the view using the ng-controller directive. This directive associates a controller with a portion of the HTML, defining the scope of that controller's influence. By understanding how to use ng-controller, developers can create modular and organized AngularJS applications, where controllers are responsible for specific sections of the UI.

To optimize performance in AngularJS, caching can be implemented when retrieving data from an external API. Caching involves storing previously fetched data locally so that subsequent requests for the same data can be served quickly without making additional network calls. Implementing caching strategies is an advanced technique to enhance the responsiveness and efficiency of AngularJS applications.

A controller in AngularJS is defined using the ngController directive. This directive is used to attach a controller to the HTML element it is declared on. The ngController directive takes the name of the controller as its attribute value, allowing the developer to specify which controller should be associated with a particular section of the view. Understanding how to define controllers is fundamental for organizing and managing application logic in AngularJS.

The "$digest" cycle in AngularJS is crucial for tracking changes and updating bindings in a controlled manner. During the digest cycle, AngularJS checks for changes in the model and updates the view accordingly. This automatic synchronization ensures that the UI reflects the latest changes in the underlying data model. Understanding the $digest cycle is fundamental to managing data binding effectively in AngularJS applications.

The isolation of scope in directives enhances an AngularJS application by preventing Scope Pollution. It ensures that the directive's scope is independent of the outer scope, avoiding unintended side effects and conflicts with other parts of the application. This isolation promotes modularity and maintainability in AngularJS applications, making it easier to reason about and extend the codebase.

AngularJS's Two-Way Data Binding is a key concept that integrates models and views seamlessly. With two-way data binding, changes in the model automatically update the view, and changes in the view update the model. This bidirectional communication simplifies the development process, reduces boilerplate code, and enhances the responsiveness of AngularJS applications. Understanding two-way data binding is fundamental for efficient data synchronization in AngularJS.

Using nested controllers in AngularJS can lead to increased complexity. While it allows for a more modular structure, it can make the code harder to understand and maintain. Developers need to carefully consider the trade-offs and use nested controllers judiciously to strike a balance between modularity and code clarity.